Heat oven to 350°F. Grease 2 (8- or 9-inch) round cake pans with shortening; lightly flour.
In large bowl, beat flour, sugar, baking powder, salt, milk, shortening and vanilla with electric mixer on low speed until moistened, scraping bowl occasionally. Beat on medium speed 2 minutes, scraping bowl occasionally. Add egg whites; beat 2 minutes longer, scrapping bowl occasionally. Pour batter evenly into pans.
Bake 8-inch pans 30 to 38 minutes (9-inch pans 27 to 35 minutes) or until toothpick inserted in center comes out clean. Cool in pans 10 minutes. Remove from pans; place on wire racks. Cool completely, about 1 hour. Fill and frost as desired.